Property 5

Q.

In the usual notation, the value of $∆\nabla$ is equal to

1. $∆-\nabla$

2. $∆+\nabla$

3. $\nabla -∆$

4. None of these

Q. $If{\int }_0^{x}f\left(t\right)dt=x+{\int }_x^{1}tf\left(t\right)dt,$ then the value of f (1) is

1. $\frac{1}{2}$
2. $0$
3. $1$
4. $-\frac{1}{2}$

Q. If f(x) is a differentiable function and ${\int }_0^{x^3}{t}^{2}f\left(t\right)dt=\frac{3}{13}{x}^{13}+5$ then $f\left(\frac{8}{27}\right)$

1. $\frac{8}{27}$
2. $\frac{16}{27}$
3. $\frac{16}{81}$
4. $\frac{8}{9}$